This document discusses parabolas and their key characteristics. It defines a parabola as the set of all points equidistant from a fixed point (the focus) and line (the directrix). The vertex is the point halfway between the focus and directrix. Parabolas can be graphed from their standard form equations, which specify the direction of opening, vertex, focus, and latus rectum (distance between focus and directrix). The document provides examples of reducing parabola equations to standard form and extracting properties of the parabola to graph it.

1. PRE-CALCULUS

2. •CONIC
SECTIONS
(Parabola)

3. Parabola
LEARNING COMPETENCY
 LC 4 Define a parabola
 LC 5 Graph parabola given an equation in vertex form
LEARNING TARGETS
 I can give the meaning of a parabola;
 I can determine the standard form of equation of a parabola; and
 I can graph a parabola in a rectangular coordinate system.

4. Parabola
A parabola is one of the conic sections. We have
already seen parabolas which open upward or
downward, as graphs of quadratic functions. Here, we
will see parabolas opening to the left or right.
Conic Sections

5. Parabola
A parabola is formed by intersecting the
plane through the cone and the top of the
cone. Parabolas can be the only conic
sections that are
considered functions because they pass the
vertical line test.
A parabola is the set of all points in a plane
that are equidistant from a fixed line, the
directrix, and a fixed point, the focus, that is
not on the line

6. Parabola
Write each of the following equations of parabolas in general form.
a. (y-3)2=48x b. x2=-36(y+1) c. (y+200)2=2500(x-150)

7. Parabola
Reduce each of the following equations of parabolas in standard form.
a. x2-4x-16y+4=0 b. x2-2x+12y-35=0 c. 4y2+96x+4y+97=0

8. Parabola Parts of a Parabola
1. The fixed point F is called the FOCUS.
2. The fixed line D is called the DIRECTRIX.
3. The point on the parabola which is halfway from the focus to the
directrix is the called VERTEX.
4. The axis of symmetry (axis of parabola) is the line passing through the
focus and perpendicular to the directrix. This axis divides the parabola
into two equal branches.
5. A chord connecting any two points of a parabola and passing through
the focus is a focal chord. Focal chord connecting two points of the
parabola passing through the focus and perpendicular to the axis of
symmetry is called the latus rectum.
Important Lengths and Distances Involved in a Parabola.
1. a= distance from vertex to focus or from vertex to directrix
2. 2a= distance from focus to an end of latus rectum or directrix.
3. 4a= length of latus rectum.

9. GENERAL FORMS OF PARABOLA
VERTICAL AXIS OF SYMMETRY 𝒙𝟐
+ 𝑫𝒙 + 𝑬𝒚 + 𝑭 = 𝟎
HORIZONTAL AXIS OF SYMMETRY 𝒚𝟐
+ 𝑫𝒙 + 𝑬𝒚 + 𝑭 = 𝟎
STANDARD FORMS OF PARABOLA
Opening of the
Graph
Right Opening Left Opening Upward Opening Downward Opening
VERTEX (0,0) 𝒚𝟐
= 𝟒𝒂𝒙 𝒚𝟐
= −𝟒𝒂𝒙 𝒙𝟐
= 𝟒𝒂𝒚 𝒙𝟐
= −𝟒𝒂𝒚
VERTEX (h,k) (𝒚 − 𝒌)𝟐= 𝟒𝒂(𝒙 − 𝒉) (𝒚 − 𝒌)𝟐= −𝟒𝒂(𝒙 − 𝒉) (𝒙 − 𝒉)𝟐= 𝟒𝒂(𝒚 − 𝒌) (𝒙 − 𝒉)𝟐= −𝟒𝒂(𝒚 − 𝒌)
𝑭: (𝒉 + 𝒂, 𝒌)
𝑳𝑹: (𝒉 + 𝒂, 𝒌 ± 𝟐𝒂)
𝑭: (𝒉 − 𝒂, 𝒌)
𝑳𝑹: (𝒉 − 𝒂, 𝒌 ± 𝟐𝒂)
𝑭: (𝒉, 𝒌 + 𝒂)
𝑳𝑹: (𝒉 ± 𝟐𝒂, 𝒌 + 𝒂)
𝑭: (𝒉, 𝒌 − 𝒂)
𝑳𝑹: (𝒉 ± 𝟐𝒂, 𝒌 − 𝒂)
EQUATION OF DIRECTRICES
𝒙 = 𝒉 − 𝒂 𝒙 = 𝒉 + 𝒂 𝒚 = 𝒌 − 𝒂 𝒚 = 𝒌 + 𝒂

10. Parabola
For each equation of the parabola, reduce to its standard form then find
the direction of its opening, vertex, focus, and endpoints of the latus
rectum. Determine the equation of the directrix and draw the parabola.
a. y2-16x=0

11. Parabola
For each equation of the parabola, reduce to its standard form then find
the direction of its opening, vertex, focus, and endpoints of the latus
rectum. Determine the equation of the directrix and draw the parabola.
c. y2+16x-32=0

12. Activity 1.4
For each equation of the parabola find the value of D, E and F.
a. y2=-4x
b. x2=-12(y+1)
c. (y-1/2)2=-12(y+1)
For each equation of the parabola, reduce to its standard form then find the
direction of its opening, vertex, focus, and endpoints of the latus rectum.
Determine the equation of the directrix and draw the parabola.
d. x2-2x-24y-47=0
e. y2-12x+4y+4=0